Studying of Dynamic Shrinking Strategy for Handling Equality Constraints.pdfVIP

Studying of Dynamic Shrinking Strategy for Handling Equality Constraints Xiao-Feng Xie * The AdaptiveBox Studio, Technical report ADBOX_2003_01 Part of this work was done in Institute of Microelectronics, Tsinghua University, Beijing, China *Email: xiexiaofeng@tsinghua.org.cn Abstract. To enhance the quality of solutions for the problems with equality constraints in evolutionary optimization, a paradigm of multi-stage dynamic shrinking strategy (MS-DSS) is proposed by partitioning the evolutionary process into three stages: a) exploring, b) approaching, and c) exploiting stage, to shrink the violation values to an expected value at the end of evolution. The experiments on three benchmark functions by evolutionary algorithm with MS-DSS produce satisfaction results, by comparing to the results of ASCHEA. Key words: constraint-handling, evolutionary computation, global optimization 1. Introduction n Generally, a constrained optimization problem can be defined as finding x ∈S ⊆R such that  f (x ) min{ f (y ); y ∈S },  g i (x ) ≤0, for i ∈[1, q ] (1)  h (x ) 0, for j [q 1, m ] ∈ +  j Where = (x ,..., x ,..., x ) T (d ∈[1, D]), x ∈[ l , u ], l and u are lower and upper boundary values. f is objective x 1 d D d d d d d function , g and h are inequality and equality